The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion.
(a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take to be an estimate of the initial relative growth rate.)
(b) Use the logistic model to estimate the world population in the year 2000 and compare with the actual population of 6.1 billion.
(c) Use the logistic model to predict the world population in the years 2100 and 2500.
(d) What are your predictions if the carrying capacity is 50 billion?